Free Printable Continuity

1.

A function is continuous at a numberc if and only if f(c) = lim f(x) as x approaches a number c.

a)

TRUE

b)

FALSE

2.

One of the conditions a function must satisfy to be continuous at a c number is "f(c) must exist"

a)

TRUE

b)

FALSE

3.

Is the function $f\left(x\right)=x^2-2x+1$ , continuous at x=0?

a)

yes

b)

no

4.

Is the function continuous at x=0?

a)

Continuous, because $\lim_{x\rightarrow0}f\left(x\right)=f\left(0\right)=-\frac{7}{2}$

b)

Discontinuous, because $\lim_{x\rightarrow0^-}f\left(x\right)=-\frac{7}{2}\ne\lim_{x\rightarrow0^+}f\left(x\right)=-2$

5.

At what x-value does this function have an infinite discontinuity?

a)

$-2$

b)

$2$

c)

$-4$

d)

$0$

6.

Is f(x) continuous at x = a, and why?

a)

No, $\lim_{x\rightarrow a^-}f\left(x\right)\ne\lim_{x\rightarrow a^+}f\left(x\right)$

b)

No, $\lim_{x\rightarrow a}f\left(x\right)\ne f\left(a\right)$

c)

Yes, $\lim_{x\rightarrow a^-}f\left(x\right)=\lim_{x\rightarrow a^+}f\left(x\right)$

d)

Yes, $\lim_{x\rightarrow a}f\left(x\right)=f\left(a\right)$

7.

in what value of x does the following function is discontinuous?

a)

3

b)

-3

c)

6

d)

-6

8.

In what value of x will the following function discontinuous?

a)

-1

b)

-2

c)

-3

d)

-4

9.

A polynomial function is continuous to all real numbers.

a)

TRUE

b)

FALSE

10.

The funciton f(x) = x²-2x+1, continuous to the interval [-7,7]

a)

TRUE

b)

FALSE

11.

A piecewise function is continuous to any any interval.

a)

TRUE

b)

FALSE

12.

Is sine function continuous over real numbers?

a)

No

b)

Yes

13.

Is cosine function continuous over real numbers?

a)

Yes

b)

No

14.

At which points Greatest integer function is not continuous?

a)

Integers

b)

Decimals

c)

negative integers

d)

Naturlal numbers

15.

Where is the function tanx continous?

a)

contionous over real numbers

b)

continuous everywhere except at the points

k\pi,k\epsilon Z

c)

continuous everywhere except at the points $\frac{k\pi}{2\ },k\epsilon Z$

d)

continuous everywhere except at 0

Continuity

Total questions: 15

Worksheet time: 9mins

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